5Dr. Liam Chen is comparing artifact distributions in 4 villages. Village populations were 180, 240, 300, and 360. He wants to divide each village into clans with the same number of members, minimizing clan size while maximizing uniformity. What is the largest possible clan size that divides all four populations exactly?

Thu, 16 Apr 2026 18:27:07 +0000

Title: Finding the Largest Uniform Clan Size Across Four Villages Using Greatest Common Divisor When analyzing cultural structures in traditional communities, one key challenge is determining how to equitably divide populations into clans—groups with equal membership—while preserving fairness and minimizing clan size. Dr. Liam Chen, a researcher in comparative anthropology, explored this problem by examining four villages with distinct populations: 180, 240, 300, and 360 residents. His goal was to recommend the largest possible clan size that evenly divides each village’s population, ensuring uniformity and respect for cultural norms. To determine the largest clan size that divides all four village populations exactly, Dr. Chen relied on a fundamental concept in number theory: the greatest common divisor (GCD). The GCD of a set of numbers is the largest positive integer that divides each number without leaving a remainder. By computing the GCD of 180, 240, 300, and 360, Chen identified the most efficient clan size that maintains consistency across all communities. Step-by-step GCD Calculation: